Small Deviations, Comparison Theorems, and Laplace Transforms
for the $L_2$ norm of a stochastic process |
Jan Hannig
Statistics Department
Colorado State University
Monday, 23 February 2004
4:10 PM
E202 Engineering Building
ABSTRACT
We consider the Laplace transforms of L2 norms of Gaussian stochastic
processes. Except for some special cases, exact Laplace transforms are, in
general, rarely obtained. It is the purpose of this talk to show that for
many Gaussian random processes the Laplace transform can be expressed in
terms of well understood functions using complex-analytic theorems on
infinite products, in particular, the Hadamard Factorization Theorem. The
second part of the talk concerns the generalization of comparison theorem of
Li (1992) to more sums of general random variables.
Refreshments will be served at 3:45 p.m. in Room 008 of the Statistics
Building
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